There is a norm on covariance matrices defined by the Frobenious norm. http://mathworld.wolfram.com/FrobeniusNorm.html Can this be used to define a valid distance between two multivariate gaussian distributions ? Something like $d^{2}\left(\mathcal{N}\left(\mu_{1},\Sigma_{1}\right),\mathcal{N}\left(\mu_{2},\Sigma_{2}\right)\right) = ||\mu_{1}-\mu_{2}||_{F}^{2} + ||\Sigma_{1}-\Sigma_{2}||_{F}^{2}$. I am looking for references / articles.
2026-03-26 14:40:40.1774536040
Frobenius norm induced distances between distribution inputs
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